life Article Life in The Context of Order and Complexity Christian Mayer Institute of Physical Chemistry, CENIDE, University of Duisburg-Essen, 45141 Essen, Germany; [email protected]; Tel.: +49-0201-183-2570 Received: 13 December 2019; Accepted: 16 January 2020; Published: 18 January 2020 Abstract: It is generally accepted that life requires structural complexity. However, a chaotic mixture of organic compounds like the one formed by extensive reaction sequences over time may be extremely complex, but could just represent a static asphalt-like dead end situation. Likewise, it is accepted that life requires a certain degree of structural order. However, even extremely ordered structures like mineral crystals show no tendency to be alive. So neither complexity nor order alone can characterize a living organism. In order to come close to life, and in order for life to develop to higher organisms, both conditions have to be fulfilled and advanced simultaneously. Only a combination of the two requirements, complexity and structural order, can mark the difference between living and dead matter. It is essential for the development of prebiotic chemistry into life and characterizes the course and the result of Darwinian evolution. For this reason, it is worthwhile to define complexity and order as an essential pair of characteristics of life and to use them as fundamental parameters to evaluate early steps in prebiotic development. A combination of high order and high complexity also represents a universal type of biosignature which could be used to identify unknown forms of life or remnants thereof. Keywords: order; complexity; origin of life; evolution; molecular evolution; prebiotic chemistry; biosignature 1. Estimating System Complexity Among the many approaches to determine system complexity as a parameter, the idea originally developed by Andrey Nikolaevich Kolmogorov seems to be most appropriate to characterize life [1–4]. It is based on the assumption that, for every structure, there is a minimal size of an algorithm (or computer program) which fully describes its entity and all of its details. The size of this computer algorithm in a universal description language in bytes may serve as a measure for the degree of complexity of the system. Even though it is hard or even impossible to determine the minimal size of the algorithm exactly (a problem known as Chaitin’s incompleteness theorem [5]), this number still can be approached and estimated for a given system. As an example, let us consider a sodium chloride crystal. Even if this crystal is of microscopic size, it may still take Tbytes to describe the position of every single ion in space. However, using a suitable computer algorithm, one may derive every single ion position by simply programming a three-dimensional repetition of the cubic elementary cell limited by the outer dimensions of the crystals. Such a computer program would include loops which are repeated over and over, but basically contain the same information as the one for a single elementary cell. Hence, it may actually be reduced to a few bytes. This means that a single crystal of e.g., sodium chloride is actually very low in structural complexity (Figure1, horizontal axis). In case of a fluid phase state such as liquids and gases, the given complexity approach does not focus on the temporary position and orientation of individual molecules. Instead, it accounts for time averaging by transversal and rotational diffusion, such that Life 2020, 10, 5; doi:10.3390/life10010005 www.mdpi.com/journal/life Life 2020, 10, 5 2 of 8 theseLife 2020 states, 10, 5 are of very low complexity as well (the time scale of averaging being adapted to biochemical2 of 8 rate constants). asphalt (products of unorganized (bytes) intelligence Life reactions) (or structures formed by life) multicellular organisms (e.g. human genome: 809 Mbytes, 1.5% encoding) reciprocal entropy of a living cell reciprocal entropy of a homogenized cell minimal genome of a living cell: 93 kbytes viruses Kolmogorov system complexity gases..………….……………………………………………………….……….………..…. liquids solids single crystal structural order / reciprocal entropy (K/J) Figure 1. Diagram showing life and other systems in the context of complexity and order. The lower limitsFigure of 1. the Diagram field of life showing are defined life and by theother information systems in content the context of the smallestof complexity genome and of order. microorganisms The lower andlimits by theof minimumthe field of thelifereciprocal are defined entropy by ofthe a livinginformation cell. Every content known of livingthe smallest organism genome falls into of thismicroorganisms category. On and the otherby the hand, minimum every of single the reciprocal system found entropy in this of a category living cell. is eitherEvery lifeknown itself living or a structureorganism formed falls into by life.this category. On the other hand, every single system found in this category is either life itself or a structure formed by life. Chaotic mixtures on the other hand may be very complex. 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Ofmay course, exist, multicellular but they are organisms usually aredepending of significantly on bi higheromolecules complexity. in their A humanenvironment genome or consists on other of approximatelyorganisms, as threein case billion of viruses. base pairs Of whichcourse, comprise multicellular about organisms 809 Mbyte are of storedof significantly information. higher As littlecomplexity. as 1.5% ofA thishuman information genome may consists be transformed of approximately into protein three structures, billion base while pairs the which vast majority comprise is reservedabout 809 for Mbyte regulation of stored of gene informatio expression,n. As for little chromosome as 1.5% of architecturethis information or may may not be serve transformed any purpose into atprotein all [7]. structures, So the actual while value the for vast complexity majority of is the reserved human genomefor regulation may be of somewhere gene expression, between 12for chromosome architecture or may not serve any purpose at all [7]. So the actual value for complexity of the human genome may be somewhere between 12 and 800 Mbytes, which of course is a very rough estimation. However, this is at least a hundred times larger than the value for Nanoarchaeum equitans mentioned above. Life 2020, 10, 5 3 of 8 and 800 Mbytes, which of course is a very rough estimation. However, this is at least a hundred times larger than the value for Nanoarchaeum equitans mentioned above. 2. Estimating Structural Order The term “order” refers to the state of a system from a largely human perspective